The associative forms of the graded Cartan type Lie superalgebras (Q2767351)

The authors determine the Cartan type Lie superalgebras that possess a nonsingular associative form. This extends to Lie superalgebras work of \textit{R. Farnsteiner} [Trans. Am. Math. Soc. 295, 417-427 (1986; Zbl 0591.17009)] for Lie algebras. The only Lie superalgebras of type \(W\) or \(S\) possessing a nonsingular associative form are Lie algebras, but for characteristic \(p>2\) all superalgebras of type \(H\) possess such a form, as do algebras \(K(m,n, {\mathbf t})\) if and only if \(m-n+5 \equiv 0\pmod p\).